Small-scale Fading Distribution Research Articles

Performance and Optimization of Outage Probability in CBTC Systems

The performance of two Access Points (APs) Communication-Based Train-Control (CBTC) systems subjected to an imperfect channel state information (CSI) scenario is investigated. More precisely, we first model the realistic small-scale fading distribution for which the receiver only has the outdated CSI due to the mobility of the train. We then derive the Outage Probability (OP) of the train and the ergodic capacity of the system in the closed-form expression based on the considered channel model. Additionally, we formulate an optimization problem that minimizes the maximal OP, which corresponds to the location of the train. For such, the signal-to-noise-ratio (SNR) is minimized as a function of the position of two APs. The pattern search method is utilized to solve the considered minimization problem. Numerical results confirm that by the optimal placement of the position of APs, the OP can be significantly ameliorated compared to the other placement methods. Furthermore, the numerical results also illustrate that the proposed solution completely coincides with the exhaustive search but with much less computation time. Finally, the mathematical framework is verified extensively by Monte Carlo simulations.

Channel Measurement and Modeling of the Small-Scale Fading Characteristics for Urban Inland River Environment

In this study, radio channel measurements were conducted in an urban inland river environment at 5.9GHz. The measurements consisted of both the line of sight (LOS) and non-line of sight (NLOS) cases. We estimate and model channel characteristics based on the measured data. For small-scale fading properties, best fit small-scale fading distribution is determined. Statistical models of the Ricean K-factors and Weibull shape parameters are provided. In addition, a distance-dependent Ricean K-factor model for the urban inland river environment is proposed. For the power delay profile (PDP), we perform cluster identification and obtain the cumulative distribution function (CDF) of the inter-cluster interval. A statistical model of the intracluster decay time constant is also presented, and an exponential decay model is applied for modeling the inter-cluster decay of the PDP. For delay spread and Doppler spread, the root mean square (RMS) delay spreads in the LOS case are compared with those in the NLOS case. Moreover, we estimate and analyze RMS Doppler spreads in both the LOS and NLOS cases. Finally, a bimodal Gaussian mixture distribution (BGMD) is employed to characterize the RMS delay spreads and RMS Doppler spreads. The BGMDs exhibit good matching levels.

Measurement‐based V2V radio channel analysis and modelling for bridge scenarios at 5.9 GHz

In this study, vehicle-to-vehicle (V2V) radio channel measurements at 5.9 GHz were conducted on a suspension bridge and a beam bridge. Given that a different structure of the two bridges will result in different channel properties, the authors study small-scale and large-scale propagation characteristics for the bridge scenarios based on measurement data. By using Akaike's information criteria, the study determines optimal small-scale fading distribution. Owing to that Ricean distribution occupies the dominant position, Ricean K-factors in the two bridge scenarios are modelled separately and compared with each other. Afterwards, power delay profiles, Doppler power spectral densities, root-mean-square (RMS) delay spread and RMS Doppler spread are estimated and analysed in different cases. They employ bimodal Gaussian mixture distribution (BGMD) to model the RMS delay spreads and the RMS Doppler spreads. Fitting results of the BGMDs show good matching levels. For the large-scale propagation characteristics, path loss model for the beam bridge scenario is proposed based on the two-ray theory. On the other hand, path loss for the suspension bridge scenario is modelled by using an empirical function derived from WINNER II. Finally, grey relational grade–mean absolute percentage error, and RMS error criteria prove the effectiveness of the two proposed path loss models.

Vehicle-to-Vehicle Propagation Channel Performance for Overtaking Cases Based on Measurements

Overtaking case is a common traffic situation, but it is likely to pose a threat to traffic safety. To ensure reliable communication, it is necessary to study the characteristics of wireless channel under overtaking cases. In this paper, we focus on Vehicle-to-Vehicle (V2V) radio channel characteristics based on measurements at 5.9GHz. Through research and analysis, we can present empirical results of propagation channels in four scenarios. Our main concern is the difference in channel characteristics between overtaking and non-overtaking case. We propose a method to divide overtaking cases and non-overtaking cases points based on small-scale fading distribution, and results show that the dividing point is about 11 meters between the measured vehicles. Judging by Akaike Information Criterion(AIC), Weibull distribution is best under overtaking cases, while it follows Ricean distribution under non-overtaking. Then, we prove that the result of the AIC decision is valid by the Kolmogorov-Smirnov test. Therefore, we further compare Weibull $\beta $ -factor and Ricean K-factor under two cases. The values of root-mean-square (RMS) delay spreads and average fade duration under overtaking cases are higher than those under non-overtaking, but RMS Doppler spreads and the level crossing rate are smaller than those under non-overtaking. The cross-correlation between RMS delay spread and Ricean K-factor is also calculated. The correlation value in OT case is higher than that in NOT case. The value of the correlation in the case of overtaking is higher than the case of non-overtaking. By comparing the above methods, it is proved that the dividing point between overtaking cases and non-overtaking cases is effective.

Performance Analysis for User-Centric Dense Networks With mmWave

This paper focuses on the coverage probability and ergodic capacity for millimeter wave (mmWave) user-centric dense networks, where multiple access points (APs) consist of a virtual cell for each user equipment and transmit data with mmWave antennas cooperatively. All APs are distributed according to a homogeneous Poisson point process. Different from the low-frequency band (below 3 GHz), blockages have a non-negligible effect on mmWave band. To illustrate the effect, we utilize a line-of-sight probability function, which is dependent on the link-length. Then, via stochastic geometry, the expressions for coverage probability and ergodic capacity are derived, which accounts for: blockages, different small-scale fading distributions (Nakagami, Rayleigh, and no fading), and AP cooperation. In addition, we deduce the approximate expressions for coverage probability and ergodic capacity by using the noise-limited approximation. The numerical results validate our analytical expressions and show that the AP cooperation can provide high coverage performance and distinct capacity gain in a lower-AP-density region.

Measurement-Based Characterization of Train-to-Infrastructure 2.6 GHz Propagation Channel in a Modern Subway Station

Channel characterization is essential when planning wireless communication deployments. We consider the wireless channel characterization in a modern subway station and its corresponding entrance tunnel, a topic greatly overlooked in the literature. We setup a Long-Term Evolution (LTE) Evolved NodeB (eNodeB) transmitter in the middle of the platform of a modern station in the Madrid Metro, Spain, to cyclically transmit frequency-division duplex (FDD) LTE signals at a carrier frequency of 2.6 GHz with a bandwidth of 10 MHz. Two receivers were used to investigate both the eNodeB-train and the eNodeB-mobile links. The train was moving at a constant speed of 18 km/h from the entrance tunnel until it is completely stopped at the end of the station. Using the multipath components extracted with the space-alternating generalized expectation-maximization (SAGE) algorithm, we characterized the wireless channel response for both links based on the following parameters: power delay profile, root mean square delay spread, Doppler power spectral density, small-scale fading distribution, and K-factor.

Performance Limits of Network Densification

Network densification is a promising cellular deployment technique that leverages spatial reuse to enhance coverage and throughput. Recent work has identified that at some point ultra-densification will no longer be able to deliver significant throughput gains. In this paper, we provide a unified treatment of the performance limits of network densification. We develop a general framework, which incorporates multi-slope pathloss and the entire space of shadowing and small scale fading distributions, under strongest cell association in a Poisson field of interferers. First, our results show that there are three scaling regimes for the downlink signal-to-interference-plus-noise ratio (SINR), coverage probability, and average per-user rate. Specifically, depending on the near-field pathloss and the fading distribution, the user performance of 5G ultra dense networks (UDNs) would either monotonically increase, saturate, or decay with increasing network density. Second, we show that network performance in terms of coverage density and area spectral efficiency can scale with the network density better than the user performance does. Furthermore, we provide ordering results for both coverage and average rate as a means to qualitatively compare different transmission techniques that may exhibit the same performance scaling. Our results, which are verified by simulations, provide succinct insights and valuable design guidelines for the deployment of 5G UDNs.

Robust Relay Selection for Large-Scale Energy-Harvesting IoT Networks

We consider the relay selection problem in large-scale energy harvesting (EH) networks. It is known that if channel state information (CSI) is available at EH relays, a diversity order equal to the number of relays can be obtained, however, at the penalty of a feedback overhead (necessary to obtain accurate CSI) which is not suitable for energy-limited devices intended, e.g., for Internet-of-Things applications. In this paper, we therefore propose a new EH relay selection scheme which is based on the residual energy at each relay’s battery, and on information on the distribution of the channels between relays and the destination. The method thus minimizes both the outage probability and the feedback cost. Where previous work relay selection based on channel distribution information consider only small-scale fading distribution, we employ a stochastic geometry approach to consider jointly the geometrical distribution (i.e., large-scale fading) and small-scale fading yielding a simple relay selection criterion that furthermore utilizes only rough information on the relay’s location, i.e., an ordinal number from the destination. The outage probability of the proposed relay selection scheme is analytically derived, and the achievable diversity order of the proposed approach is investigated. Computer simulations confirm our theoretical analyses and show that our approach is robust against errors in the estimation of the distances between nodes.

Analysis of Small-Scale Fading Distributions in Vehicle-to-Vehicle Communications

This work analyzes the characteristics of the small-scale fading distribution in vehicle-to-vehicle (V2V) channels. The analysis is based on a narrowband channel measurements campaign at 5.9 GHz designed specifically for that purpose. The measurements were carried out in highway and urban environments around the city of Valencia, Spain. The experimental distribution of the small-scale fading is compared to several analytical distributions traditionally used to model the fast fading in wireless communications, such as Rayleigh, Nakagami-m, Weibull, Rice, andα-μdistributions. The parameters of the distributions are derived through statistical inference techniques and their goodness-of-fit is evaluated using the Kolmogorov-Smirnov (K-S) test. Our results show that theα-μdistribution exhibits a better fit compared to the other distributions, making its use interesting to model the small-scale fading in V2V channels.

Optimizing Content Caching to Maximize the Density of Successful Receptions in Device-to-Device Networking

Device-to-device (D2D) communication is a promising approach to optimize the utilization of air interface resources in 5G networks, since it allows decentralized opportunistic short-range communication. For D2D to be useful, mobile nodes must possess content that other mobiles want. Thus, intelligent caching techniques are essential for D2D. In this paper we use results from stochastic geometry to derive the probability of successful content delivery in the presence of interference and noise. We employ a general transmission strategy where multiple files are cached at the users and different files can be transmitted simultaneously throughout the network. We then formulate an optimization problem, and find the caching distribution that maximizes the density of successful receptions (DSR) under a simple transmission strategy where a single file is transmitted at a time throughout the network. We model file requests by a Zipf distribution with exponent $\gamma_r$, which results in an optimal caching distribution that is also a Zipf distribution with exponent $\gamma_c$, which is related to $\gamma_r$ through a simple expression involving the path loss exponent. We solve the optimal content placement problem for more general demand profiles under Rayleigh, Ricean and Nakagami small-scale fading distributions. Our results suggest that it is required to flatten the request distribution to optimize the caching performance. We also develop strategies to optimize content caching for the more general case with multiple files, and bound the DSR for that scenario.

Human Body Affected Small-Scale Fading for Indoor UWB Channel

This paper deals with the small-scale fading distribution for UWB channels in the absence and presence of human bodies in indoor line-of-sight (LOS) environments and performance analysis of UWB systems considering the small-scale fading distribution. To obtain small-scale fading statistics, the channel measurements are performed in five representative environments that have different structure and size while locating the receiver (Rx) antenna on 49 (7×7 grid) local points with a fixed transmitter (Tx) antenna in each environment. The measured channel data are processed by a vector network analyzer and the target frequency bands range from 3 to 4.6GHz. From the measured data, we find the best fitted channel model among several typical theoretical distribution models such as Lognormal, Nakagami, and Weibull distributions, showing good agreement with the empirical channel data. We analyze the amplitude variation of the small-scale fading distribution in the absence and presence of human bodies. The results show that the small-scale fading statistics are best described by Weibull distribution and the two parameters of the distribution that determine the shape and the scale of the distribution depend on whether or not human bodies exist. We modeled and analyzed two parameters at different excess delays for all environments. Based on the measured small-scale fading distribution, this paper deals with the performance of UWB system using Rake receivers and also compares the performance with the existing channel model. The results suggest that the small-scale fading distribution in the absence and the presence of human bodies in indoor LOS environments should be considered when assessing the performance of UWB systems.

A reverberation chamber for rodents’ exposure to wideband radiofrequency electromagnetic fields with different small-scale fading distributions

A reverberation chamber (RC) is realized for the rodents’ in vivo exposure to electromagnetic fields (EMFs) with various small-scale fading characteristics. Its performance is evaluated to ensure the exposure experiments from 0.85 to 2.60 GHz. By different configurations, line-of-sight and non-line-of-sight exposures can be established. The measured electric field in the RC is analyzed to determine its statistical distribution. We accordingly reconstruct the EMF environment by numerical methods. Simulations are carried to compare the dosimetric variability due to different small-scale fading characteristics. It demonstrates that the surveyed fading distribution will not change the specific absorption rate in the rats. The possibility to reproduce the realistic multi-reflective EMF environment by adjusting the structures of the RC is discussed. It is the first reported in vivo exposure system aiming to provide the EMF exposure with different small-scale fading distributions.

Corrections to “Unified Laguerre Polynomial-Series-Based Distribution of Small-Scale Fading Envelopes” [Oct 09 3988-3999

In this correspondence, we point out two typographical errors in Chai and Tjhung's paper, and we offer the correct formula of the unified Laguerre polynomial-series-based cumulative distribution function (cdf) for small-scale fading distributions. A Laguerre polynomial-series-based cdf formula for noncentral chi-square distribution is also provided as a special case of our unified cdf result.

Experimental Characterization and Modeling of Outdoor-to-Indoor and Indoor-to-Indoor Distributed Channels

We propose and parameterize an empirical model of the outdoor-to-indoor and indoor-to-indoor distributed (cooperative) radio channel, using experimental data in the 2.4-GHz band. In addition to the well-known physical effects of path loss, shadowing, and fading, we include several new aspects in our model that are specific to multiuser distributed channels: 1) correlated shadowing between different point-to-point links, which has a strong impact on cooperative system performance; 2) different types of indoor node mobility with respect to the transmitter and/or receiver nodes, implying a distinction between static and dynamic shadowing motivated by the measurement data; and 3) a small-scale fading distribution that captures more severe fading than that given by the Rayleigh distribution.

Unified Laguerre Polynomial-Series-Based Distribution of Small-Scale Fading Envelopes

We derive new unified probability density function (pdf) formulas based on the generalized Laguerre polynomial series expansion that cover a wide range of small-scale fading distributions in wireless communications. The unified envelope pdf covers many known Laguerre polynomial-series-based pdf's and small-scale fading distributions, which include the multiple-waves-plus-diffuse-power (MWDP) fading, kappa-mu, Nakagami-m, Rician (Nakagami-n), Nakagami-q (Hoyt), Rayleigh, Weibull, and alpha-mu (Stacy) distributions as special cases. We highlight that the unified pdf formulas are general and applicable to characterize the distribution of any random variable defined on the positive range. We then propose two truncated forms of the pdf and prove that the original pdf and both truncated forms satisfy the properties of a valid pdf. A new cumulative distribution function and a moment-generating function of this pdf are derived. We also analyze the truncation error for the case when only a finite number of terms are kept in the series expansion.

Ultrawideband Channel Modeling on the Basis of Information-Theoretic Criteria

We present results of two indoor ultrawideband channel measurement campaigns in the 2-5 GHz frequency band. In measurement campaign I (MC I), the channel is static and we sample it spatially, while in MCII the transmitting and receiving antennas are fixed and channel variation is induced by people moving in the environment. Transmitter and receiver are separated by up to 27 m in MC I and up to 20 m in MC II. To determine suitable small-scale fading distributions for the tap amplitudes of the discrete-time baseband-equivalent channel impulse response, we use Akaike's information criterion (AIC). Despite the large bandwidth, AIC supports the Rayleigh (MCI) or the Rice distribution (MC II). For data from MC II, we estimate the covariance matrix of the random channel impulse response and demonstrate that the number of corresponding significant eigenvalues, and hence the diversity order of the channel, scales approximately linearly with bandwidth. Contrary to the uncorrected scattering assumption, we find that the channel taps are weakly correlated. The ergodic capacity predicted by the Ricean channel model with parameters estimated from MC II shows good agreement with the ergodic capacity obtained by direct evaluation of the measurement results, while the corresponding outage capacities show a worse fit for low outage probabilities because of shadowing.